If the ratio of $b$ to $a$ is 3, then what is the value of $a$ when $b=12-5a$?
The given ratio tells us that $\frac{b}{a}=3$ or that $b=3a$. We substitute this value for $b$ so we have an equation with only one variable. We find  \begin{align*}
3a&=12-5a \\
\Rightarrow \quad 8a&=12 \\
\Rightarrow \quad a &= 12/8 \\
\Rightarrow \quad a &= \boxed{\frac{3}{2}}.
\end{align*}